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rashmi

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These are questions asked by rashmi

I need this plot...

rashmi 55 Maple
plot syntax plotting
December 07 2022
1 0

> expr[[(-.684-1.08*r+6.1*r^2-2*r^3+0.36e-1*ln(10.*r)-.3*r^2*ln(10.*r))/(-1.14+1.2*r+0.6e-1*ln(10.*r)), 1.290994449*sqrt((-.1296*r+1.512*r^2-.36*r^3+6.1*r^4-2*r^5-0.72e-1*r^2*ln(10.*r)-.3*r^4*ln(10.*r)+(-.684-1.08*r+6.1*r^2-2*r^3+0.36e-1*ln(10.*r)-.3*r^2*ln(10.*r))*(.216*r-2.52*r^2+.12*r^2*ln(10.*r))/(-1.14+1.2*r+0.6e-1*ln(10.*r)))/(-1.14+1.2*r+0.6e-1*ln(10.*r)))], [(-.684-1.08*r+6.1*r^2-2*r^3+0.36e-1*ln(10.*r)-.3*r^2*ln(10.*r))/(-1.14+1.2*r+0.6e-1*ln(10.*r)), -1.290994449*sqrt((-.1296*r+1.512*r^2-.36*r^3+6.1*r^4-2*r^5-0.72e-1*r^2*ln(10.*r)-.3*r^4*ln(10.*r)+(-.684-1.08*r+6.1*r^2-2*r^3+0.36e-1*ln(10.*r)-.3*r^2*ln(10.*r))*(.216*r-2.52*r^2+.12*r^2*ln(10.*r))/(-1.14+1.2*r+0.6e-1*ln(10.*r)))/(-1.14+1.2*r+0.6e-1*ln(10.*r)))]];
> plot([seq([expr[j][], r = 0 .. 1], j = 1 .. 2)], -6 .. 6, -10 .. 10, color = [blue, blue]);
 why I am getting error in this, please help

Plot in maple 12...

rashmi 55 Maple 12
plot parametric plotting
June 10 2022
1 3

I am trying to plot the following kind of sequence. I was expecting a curve for one set of [] inside plot command, but I am getting twin curve there. How can I get a single curve for one single parametric command there. Please reply asap.

plot([[(1.428571429*(r^2+.49-4*r*(r^2+.49-2*exp(-.1/r))/(2*r-.2*exp(-.1/r)/r^2)))*csc((1/3)*Pi), sqrt(16*r^2*(r^2+.49-2*exp(-.1/r))/(2*r-.2*exp(-.1/r)/r^2)^2+.49*cos((1/3)*Pi)^2-2.040816327*(r^2+.49-4*r*(r^2+.49-2*exp(-.1/r))/(2*r-.2*exp(-.1/r)/r^2))^2*cot((1/3)*Pi)^2), r = -10 .. 10], [(1.428571429*(r^2+.49-4*r*(r^2+.49-2*exp(-.1/r))/(2*r-.2*exp(-.1/r)/r^2)))*csc((1/3)*Pi), -sqrt(16*r^2*(r^2+.49-2*exp(-.1/r))/(2*r-.2*exp(-.1/r)/r^2)^2+.49*cos((1/3)*Pi)^2-2.040816327*(r^2+.49-4*r*(r^2+.49-2*exp(-.1/r))/(2*r-.2*exp(-.1/r)/r^2))^2*cot((1/3)*Pi)^2), r = -10 .. 10], [(5.*(r^2+0.4e-1-4*r*(r^2+0.4e-1-2*exp(-.2/r))/(2*r-.2*exp(-.2/r)/r^2)))*csc((1/3)*Pi), sqrt(16*r^2*(r^2+0.4e-1-2*exp(-.2/r))/(2*r-.2*exp(-.2/r)/r^2)^2+0.1e-1*cos((1/3)*Pi)^2-25.*(r^2+0.4e-1-4*r*(r^2+0.4e-1-2*exp(-.2/r))/(2*r-.2*exp(-.2/r)/r^2))^2*cot((1/3)*Pi)^2), r = -10 .. 10], [(5.*(r^2+0.4e-1-4*r*(r^2+0.4e-1-2*exp(-.2/r))/(2*r-.2*exp(-.2/r)/r^2)))*csc((1/3)*Pi), -sqrt(16*r^2*(r^2+0.4e-1-2*exp(-.2/r))/(2*r-.2*exp(-.2/r)/r^2)^2+0.1e-1*cos((1/3)*Pi)^2-25.*(r^2+0.4e-1-4*r*(r^2+0.4e-1-2*exp(-.2/r))/(2*r-.2*exp(-.2/r)/r^2))^2*cot((1/3)*Pi)^2), r = -10 .. 10]], -13 .. 5, -5 .. 5)

Combined plots of two functions...

rashmi 55 Maple 12
plotting
January 29 2018
1 2

Dear All,

I am having problem in plotting two function(which themselves are functions of elliptical integrals of first and third kind) together.

If I plot them separately, it has no issues but while combining it plots just one.

I am attaching the maple worksheet here, I have to plot alpha and beta together with 'z' as independent variable.

Please reply asap.
 

> 

restart
> 

a := .5:

------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

> 

b__sc := -a+2*s*sqrt(3*(3-x))*cos((1/3)*arccos(-s*sqrt(3*a/(3-x)))):
> 

d__sc := -a+2*t*sqrt(3*(3-x))*cos((1/3)*arccos(-t*sqrt(3*a/(3-x)))):

--------------------------------------------------------------------------------------------------------------------

> 

b := proc (z) options operator, arrow; s*b__sc/(1-z) end proc:
> 

d := proc (z) options operator, arrow; t*b__sca/(1-z) end proc:

--------------------------------------------------------------------------------------------------------------------

> 

w__s := proc (z) options operator, arrow; a/b(z) end proc:
> 

v__s := proc (z) options operator, arrow; a/d(z) end proc:

--------------------------------------------------------------------------------------------------------------------

> 

h__sc := proc (z) options operator, arrow; (b(z)+a)/(b(z)-a) end proc:
> 

j__sc := proc (z) options operator, arrow; (d(z)+a)/(d(z)-a) end proc:

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

> 

r := proc (z) options operator, arrow; (1/3)*x+2*sqrt(b(z)^2-a^2-(1/3)*x^2)*cos((1/3)*arccos(-(3/2)*sqrt(3)*(2*(b(z)-a)^2-(1/3)*x*(-a^2+b(z)^2)-(2/27)*x^3)/(b(z)^2-a^2-(1/3)*x^2)^(3/2)))/sqrt(3) end proc:
> 

u := proc (z) options operator, arrow; (1/3)*x+2*sqrt(d(z)^2-a^2+(1/3)*x^2)*cos((1/3)*arccos(-(3/2)*sqrt(3)*(2*(d(z)-a)^2-(1/3)*x*(-a^2+d(z)^2)-(2/27)*x^3)/(d(z)^2-a^2+(1/3)*x^2)^(3/2)))/sqrt(3) end proc:

-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

> 

H := proc (z) options operator, arrow; 1/r(z) end proc:
> 

J := proc (z) options operator, arrow; 1/u(z) end proc:

---------------------------------------------------------------------------------------------------------------------------------------------------------

> 

M := proc (z) options operator, arrow; ((h__sc(z)-2*H(z))*(6*H(z)+h__sc(z))+8*x^2/(b(z)^2*(1-w__s(z))^2))^(1/2) end proc:
> 

P := proc (z) options operator, arrow; ((j__sc(z)-2*J(z))*(6*J(z)+j__sc(z))+8*x^2/(d(z)^2*(1-v__s(z))^2))^(1/2) end proc:

---------------------------------------------------------------------------------------------------------------------------------------------------------

> 

n__1 := proc (z) options operator, arrow; evalf((1-6*H(z)/h__sc(z)+M(z)/h__sc(z))/(1-2*H(z)/h__sc(z)-(4+2*x)/(h__sc(z)*(a^2+2*x))+M(z)/h__sc(z)+sqrt((2+x)^2-4*a^2-8*x)/(h__sc(z)*(a^2+2*x)))) end proc:
> 

n__3 := proc (z) options operator, arrow; evalf((1-6*J(z)/j__sc(z)+P(z)/j__sc(z))/(1-2*J(z)/j__sc(z)-(4+2*x)/(j__sc(z)*(a^2+2*x))+P(z)/j__sc(z)+sqrt((2+x)^2-4*a^2-8*x)/(j__sc(z)*(a^2+2*x)))) end proc:

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

> 

n__2 := proc (z) options operator, arrow; evalf((1-6*H(z)/h__sc(z)+M(z)/h__sc(z))/(1-2*H(z)/h__sc(z)-(4+2*x)/(h__sc(z)*(a^2+2*x))+M(z)/h__sc(z)-sqrt((2+x)^2-4*a^2-8*x)/(h__sc(z)*(a^2+2*x)))) end proc:
> 

n__4 := proc (z) options operator, arrow; evalf((1-6*J(z)/j__sc(z)+P(z)/j__sc(z))/(1-2*J(z)/j__sc(z)-(4+2*x)/(j__sc(z)*(a^2+2*x))+P(z)/j__sc(z)-sqrt((2+x)^2-4*a^2-8*x)/(j__sc(z)*(a^2+2*x)))) end proc:

--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

> 

k := proc (z) options operator, arrow; evalf((1/2)*2^(1/2)*(h__sc(z)/M(z))^(1/2)*(M(z)/h__sc(z)+6*H(z)/h__sc(z)-1)^(1/2)) end proc:
> 

l := proc (z) options operator, arrow; evalf((1/2)*2^(1/2)*(j__sc(z)/P(z))^(1/2)*(P(z)/j__sc(z)+6*J(z)/j__sc(z)-1)^(1/2)) end proc:

----------------------------------------------------------------------------------------------------------------------------------------------------------------

> 

psi := proc (z) options operator, arrow; evalf(arcsin((1-2*H(z)/h__sc(z)-M(z)/h__sc(z))/(1-6*H(z)/h__sc(z)-M(z)/h__sc(z)))) end proc:
> 

phi := proc (z) options operator, arrow; evalf(arcsin((1-2*J(z)/j__sc(z)-P(z)/j__sc(z))/(1-6*J(z)/j__sc(z)-P(z)/j__sc(z)))) end proc:

-----------------------------------------------------------------------------------------------------------------------------------------------------------------

> 

Omega__1 := proc (z) options operator, arrow; evalf((4*(1-w__s(z))*(2+x+sqrt((2+x)^2-4*a^2-8*x))-4*a^2-8*x)/(a*((2+x)^2-4*a^2-8*x)^(1/2)*((4+2*x)/(a^2+2*x)+2*H(z)-h__sc(z)+M(z)+sqrt((2+x)^2-4*a^2-8*x)/(a^2+2*x)))) end proc:
> 

Omega__3 := proc (z) options operator, arrow; evalf((4*(1-v__s(z))*(2+x+sqrt((2+x)^2-4*a^2-8*x))-4*a^2-8*x)/(a*((2+x)^2-4*a^2-8*x)^(1/2)*((4+2*x)/(a^2+2*x)+2*J(z)-j__sc(z)+P(z)+sqrt((2+x)^2-4*a^2-8*x)/(a^2+2*x)))) end proc:

----------------------------------------------------------------------------------------------------------------------------------------

> 

Omega__2 := proc (z) options operator, arrow; evalf((4*(1-w__s(z))*(2+x+sqrt((2+x)^2-4*a^2-8*x))+8*x+4*a^2)/(a*((2+x)^2-4*a^2-8*x)^(1/2)*((4+2*x)/(a^2+2*x)+2*H(z)-h__sc(z)+M(z)-sqrt((2+x)^2-4*a^2-8*x)/(a^2+2*x)))) end proc:
> 

Omega__4 := proc (z) options operator, arrow; evalf((4*(1-v__s(z))*(2+x+sqrt((2+x)^2-4*a^2-8*x))+8*x+4*a^2)/(a*((2+x)^2-4*a^2-8*x)^(1/2)*((4+2*x)/(a^2+2*x)+2*J(z)-j__sc(z)+P(z)-sqrt((2+x)^2-4*a^2-8*x)/(a^2+2*x)))) end proc:

---------------------------------------------------------------------------------------------------------------------------------------------

> 

alpha := proc (z) options operator, arrow; evalf(-Pi+4*(Omega__1(z)*(EllipticPi(n__1(z), k(z))-EllipticPi(psi(z), n__1(z), k(z)))+Omega__2(z)*(EllipticPi(n__2(z), k(z))-EllipticPi(psi(z), n__2(z), k(z))))/((1-w__s(z))*(M(z)*h__sc(z))^(1/4))) end proc:
> 

beta := proc (z) options operator, arrow; evalf(-Pi+4*(Omega__3(z)*(EllipticPi(n__3(z), l(z))-EllipticPi(phi(z), n__3(z), l(z)))+Omega__4(z)*(EllipticPi(n__4(z), l(z))-EllipticPi(phi(z), n__4(z), l(z))))/((1-v__s(z))*(P(z)*j__sc(z))^(1/4))) end proc:
> 

plot([alpha, beta], 0 .. 1);

Warning, unable to evaluate 1 of the 2 functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

  

 
> 

``


 

Download deflection-angle-comd.mw

Plot of complete or incomplete Elliptica...

rashmi 55 Maple 7
plot integral special-function
July 05 2017
1 5

How to plot an Elliptical Function of Third kind complete or incomplete, eg. EllipticPi(n,k) if n and k are not constants?

as The function I wish to plot and explore contains Elliptical Function of Third kind complete and incomplete with complicated form of n and k.

Please reply asap.

Regards

To obtain data points from implicitplot3...

rashmi 55 Maple 12
implicitplot3d dataset
March 18 2017
1 6

Dear All,

I am plotting the following function using implicitplot command.:


plots[implicitplot3d]((17.31626331*M^3-(4*(z[1]-z[2])^2*M^2-1.171300684*(z[1]+z[2])^2)*(1.082266457-2*M)*(1.082266457-3*M))^2 = 4.598621420*(z[1]+z[2])^2*M*(1.082266457-2*M)^3*(4*(z[1]-z[2])^2*M^2-1.171300684*(z[1]+z[2])^2), M = 0 .. 1, z[1] = 0 .. 10, z[2] = -10 .. 0);

How can I extract data points from the plot obtained

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